A can work 4/3 as fast as B and C together. A and B together can work 6 times as fast as C. If all t

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25 May 2022 Time and Work

A can work 4/3 as fast as B and C together. A and B together can work 6 times as fast as C. If all three of them complete a job in 100/7 days, then how long would B alone take to complete the same work (in days)?

OPtion

1) 75
2) 60
3) 40
4) 25
5) 90
6) 80
7) 45
8) 50
9) 100
10) None of these

Solution

A, B and C together complete a job in 100/7 days
.'. 1/A + 1/B + 1/C = 7/100 ----(i)
A and B together can work 6 times as fast as C
1/A + 1/B = 6/C ----(ii)
A can work 4/3 as fast as B and C together
1/A = (4/3)*(1/B + 1/C) ⇒ 1/B + 1/C = (3/4)(1/A) ----(iii)
Substituting 1/A + 1/B = 6/C from eqn (ii) in eqn. (i), we get 6/C + 1/C = 7/100
⇒ 1/C=1/100
Substituting 1/B + 1/C = (3/4)(1/A) from eqn (iii) in eqn (i), we get 1/A + (3/4)(1/A) = 7/100
⇒ 1/A=1/25
.'. 1/25 + 1/B + 1/100 = 7/100
⇒ 1/B=1/50
Therefore, B would take 50 days to complete the work alone.

Correct Option: 8 Best Solution (0)